But if the mind actively generates perception, this raises the question whether the result has anything to do with the world, or if so, how much. The answer to the question, unusual, ambiguous, or confusing as it would be, made for endless trouble both in Kant's thought and for a posterity trying to figure him out. To the extent that knowledge depends on the structure of the mind and not on the world, knowledge would have no connection to the world and is not even true representation, just a solipsistic or intersubjective fantasy. Kantianism seems threatened with "psychologism," the doctrine that what we know is our own psychology, not external things. Kant did say, consistent with psychologism, that basically we don't know about "things-in-themselves," objects as they exist apart from perception. But at the same time Kant thought he was vindicating both a scientific realism, where science really knows the world, and a moral realism, where there is objective moral obligation, for both of which a connection to external or objective existence is essential. And there were also terribly important features of things-in-themselves that we do have some notion about and that are of fundamental importance to human life, not just morality but what he called the three "Ideas" of reason: God, freedom, and immortality. Kant always believed that the rational structure of the mind reflected the rational structure of the world, even of things-in-themselves -- that the "operating system" of the processor, by modern analogy, matched the operating system of reality. But Kant had no real argument for this -- the "Ideas" of reason just become "postulates" of morality -- and his system leaves it as something unprovable. The paradoxes of Kant's efforts to reconcile his conflicting approaches and requirements made it very difficult for most later philosophers to take the overall system seriously.

Nevertheless, Kant's theory does all sorts of things that seem appropriate for a non-reductionistic philosophical system and that later philosophy has had trouble doing at all. Kant managed to provide, in phenomenal reality (phaenomena="appearances"), for a sphere for science that was distinct and separate from anything that would relate to morality or religion. The endless confusion and conflict that still results from people trying to figure out whether or how science and religion should fit together is deftly avoided by Kant, who can say, for instance, that God and divine creation cannot be part of any truly scientific theory because both involve "unconditioned" realities, while science can only deal with conditioned realities. In the world, everything affects everything else, but the traditional view, found even in Spinoza, is that God is free of any external causal influences. Similarly, Kant can be a phenomenal determinist with science yet simultaneously allow for free will, and that in a way that will not be entirely explicable to us -- a virtue when the very idea of a rational and purposive free will, and not just arbitrary choices, has involved obscurities that no one has been able to resolve. Kant's theory prevents psychological explanations for behavior, however illuminating, being used to excuse moral responsibility and accountability. Thus, the tragic childhood of the defendant, however touching and understandable, cannot excuse crimes committed in full knowledge of their significance.

Kant's approach is also of comparative interest because of the similar ancient Buddhist philosophical distinction between conditioned realities, which mostly means the world of experience, and unconditioned realities ("unconditioned dharmas"), which interestingly include, not only the sphere of salvation, Nirvana, but also space, which of course for Kant was a form imposed a priori on experience by the mind. The connection may be more than a coincidence. Kant's theory of the Antinomies draws on the Greek Skeptics, whose founder, Pyrrhô of Elis, was with the army of Alexander the Great in India. Pyrrho returned with a principle echoing the Fourfold Negation of Buddhist philosophy. While Kant wants to resolve some of the Antinomies with Postulates of Practical Reason (i.e. presuppositions of morality), the principle remains that theoretical reason generates contradictions when applied to transcendent objects. This would be agreeable to Pyrrhô, or even to Nagârjuna.

The problems that must be sorted out with Kant are at the same time formidable. Most important is the confusion that results from Kant mixing together two entirely different theories in the Critique of Pure Reason (1781). The first theory is that the fundamental activity of the mind, called "synthesis," is an activity of thought that applies certain concepts to a previously given perceptual datum from experience. It is upon this theory that the Critique of Pure Reason was planned with its fundamental division between the "Transcendental Aesthetic," about the conditions of perception (what Kant called empirical "intuition"), and the "Transcendental Logic," about the conditions of thought. Thus, Kant still says, as late as page 91 of the first edition ("A"), "But since intuition [Anschauung] stands in no need whatsoever of the functions of thought, appearances [Erscheinungen] would none the less present objects to our intuition" (A 90-91, Norman Kemp Smith translation, 1929, St. Martin's, 1965), without, that is, any need for mental synthesis.

However, right in the middle of his subsequent argument for why certain concepts would be necessary and known a priori with respect to experience (the "Transcendental Deduction"), Kant realized that "synthesis" would have to produce, not just a structure of thought, but the entire structure of consciousness within which perception also occurs. Thus he says, "What is first given to us is appearance. When combined with consciousness [Bewußtsein], it is called perception [Wahrnehmung]" (A 119-120). It is the structure of consciousness, through synthesis, that turns "appearances" into objects and perceptions, without which they would be nothing. Consequently Kant made synthesis a function of imagination rather than thought, as a bridge between thought and perception, though this creates its own confusions (it still depends on the forms of thought and is still treated in the Logic). This move occurred because Kant hit upon the idea that synthesis produced the unity that we actually find in "apperception," i.e. in the unity of consciousness -- everything I know, think, see, feel, remember, etc. belongs to my consciousness in one temporal stream of experience. Synthesis therefore brings things into consciousness, making it possible for us to subsequently recognize that our consciousness exists and that there are things in it. Hume had described the result as "something betwixt unity and number," since it is paradoxically one thing and many things all at the same time.

One benefit of Kant's theory is that for the first time in the history of philosophy there is an explanation that can account for the simple phenomenon of sleep. Descartes apparently did not realize that when he made thought the essence of soul, this ruled out a state of non-thought for the mind, i.e. sleep or unconsciousness. This problem was first noted, as far as I am aware, by John Locke, whose fine phrase is, "'Tis doubted whether I thought all last night, or no..." The soul could cease thinking no more than matter could cease being extended (as Descartes believes). Unconsciousness, however, was as much of a theoretical challenge for the Empiricists as for the Rationalists. If the mind is the passive recipient of perception, and perception is conscious (a presence of an "idea" in the mind, according to Locke), then, again, the mind would be perpetually conscious. You can close your eyes to go to sleep, but hearing and sensation continue. You are constantly hearing that refrigerator or air-conditioning. Only with Kant's theory, of active synthesis, is consciousness an activity that may or make not take up certain sensations, or anything, into awareness. It is an activity that can simply shut down, thereby producing unconsciousness either in sleep or as the result of trauma or pathology. This is a virtue of the theory rarely noted.

These were all revolutionary ideas, exploring both the logical and the psychological principles on which the complex whole of consciousness could be generated, but they tore up Kant's original plan for his system so much that he was never quite comfortable with them. He then tried to paper over his most daring insights when he came to write both the Prolegomena to any Future Metaphysics (1783) and the changes that he introduced into the second edition of the Critique itself (1787, "B"). Thus Schopenhauer, who understood the meaning of Kant's change of approach, advised his readers that they would be wasting their time unless they obtained an edition of the Critique that included the whole text from the first edition. It is now standard to include both versions, with the original paginations in the margins.

The path to resolving the paradoxes of Kant's theory opens up with two basic realizations: (1) Kant always believed that reason connected us directly to things-in-themselves, and (2) Kant's system is not a Cartesian theory of hidden, transcendent objects, but a version of empirical realism, that we are directly acquainted with real objects. Kant's notion that reason connects us directly to things-in-themselves does not allow for speculative metaphysics as practiced by the Rationalists because reason alone does not determine any positive content of knowledge ("Thoughts without content are empty; intuitions without concepts are blind," A 51). For that some datum is required. Kant allows that we possess two sources of input that can serve as such a datum, physical sensation and the sense of moral duty. Physical sensation precipitates an application of reason to experience, producing the perception of phenomenal objects. The supreme rational expression of this is science. The sense of moral duty precipitates an application of reason that generates ethics and religion. The supreme rational expression of this is the "Postulates of Practical Reason," the "Ideas" of God, freedom, and immortality which, to Kant, are required as conditions of the Moral Law.

The differences between reality as seen in science and reality as seen in morality and religion reveal that there are aspects to existence that are not revealed by either datum alone. The two sources are also unequal in the magnitude and ultimate significance of their content. What science can investigate and know is apparently all but endless, but it still leaves us wondering, "What is it all for?" Morality and religion have a far more limited rational content, returning to many of the same issues over and over again, but such issues happen to include, not just the questions about how to live, but the ultimate questions about the meaning of life and existence ("Life, the Universe and Everything," in the memorable formula of Douglas Adams). That our moral datum does not lead to direct, positive knowledge of things that we are able to conceive, like God, leads Kant to characterize his system as transcendental idealism, that we have a subjective representation of such things, without the real intuition that we have of physical objects. The reality revealed by morality is thus for Kant a matter of faith (Glaube), an inference from the Moral Law which is itself present to us with an inexplicable authority. "Transcendental idealism" is thus profoundly different from other forms of "idealism," like the "subjective idealism" of Berkeley (what Kant called "empirical idealism") or the "objective idealism" of Hegel, both of which offer speculative certainties about the ultimate nature of things, which Kant does not do. The nature of things that we can know about concretely, for Kant, is revealed by science. Hence, Kantian transcendental idealism is equally attended by empirical realism.

How Kant can be certain that reason connects us directly to things-in-themselves is an question that he cannot answer. All that the Transcendental Deduction aimed at was showing that particular concepts, like causality or substance, are "necessary conditions for the possibility of experience." If successful, the Deduction limits the application of the concepts to experience, which is fine for Kant's philosophy of science, but doesn't help when he turns to morality and the "Postulates of Practical Reason." There his basic, but unjustified, theory of reason emerges. This shortcoming is what was directly addressed and answered by Jakob Fries, whose epistemology thus could save the generality of Kant's theory without falling back, like Hegel, into speculative metaphysics.

That Kant's theory is one of empirical realism is difficult to understand and easily forgotten. Since phenomena are undoubtedly mental contents, a point repeatedly stressed by Kant, it is natural and easy to infer from this a Cartesian "transcendental realism," according to which "real" objects, which are not mental contents, are things that we do not experience. A transcendental realism clearly contradicts Kant's transcendental idealism, but we can still be left thinking that what we really have is an empirical (subjective) idealism with a kind of transcendental agnosticism -- we don't know transcendent Cartesian objects, but they are the real objects (the Greek ontôs ónta, "beingly beings"). The lack of clear settlement in this area of basic ontology is the most intractable problem in Kant's philosophy.

The situation, however, is not unique to Kant. Something very similar can be found in Chinese T'ien-t'ai Buddhism (Japanese Tendai), as formulated by the great Chih-i (or Zhiyi, 538-597). There we find the doctrine of the "three truths" of "Emptiness" (neither existence nor non-existence nor both nor neither), "conventional existence," and "the Middle." "Emptiness" is rather like Kantian things-in-themselves where "dialectical illusion" is revealed by the Antinomies (a device similar to that employed by Nagârjuna, c.200 AD); "conventional existence" is empirical realism; and "the Middle" the Buddhist reconciliation of the two -- not a Hegelian "synthesis" because no absolute knowledge is produced to overcome the inconceivability of Emptiness.

Such a religious doctrinal tradition, however, may not be considered by many to be very helpful with modern philosophical problems; and the T'ien-t'ai "Middle," however consistent with the paradoxes of Buddhist philosophy, is not a marked improvement over the balancing act in which Kant himself leaves us. The solution to the dilemma was grasped by Schopenhauer but not otherwise well understood by Kantians: Consciousness does not just condition knowledge and perception, it conditions external reality. The modern context the most like this is in quantum mechanics, where, at least according to Niels Bohr, objects exist in a certain way, as discrete actualities, because they are observed. Otherwise, reality exists independently only as a sum of possibilities (where Schrödinger's Cat can be both dead and alive). This is not exactly what we get in Schopenhauer, who simplified matters by completely eliminating individuality from the thing-in-itself: Individuality only occurs in space, the principium individuationis. That, however, also eliminated any possibility of individual immortality, which Kant thought was rather important. I do not think, indeed, that much progress has been made beyond that. Something new is required, as suggested in The Origin of Value in a Transcendent Function, "Ontological Undecidability," and "A New Kant-Friesian System of Metaphysics." If neither subject nor object, internal nor external, are ontologically fundamental, then we can stop worrying about in which place the real things really are, and the threat of either transcendental realism or empirical idealism disappears. This again sounds like what might be needed in quantum mechanics, and a Kantian quantum mechanics could offer hope both for the physics and metaphysics.

That brings us back to the datum of morality. Indeed, Kant's whole system does seem to come down to his own famous words, inscribed on his tomb, the "starry heavens above and the moral law within." If the existence of morality is as evident as the existence of physical objects, then Kant's dualism (empirical and transcendental) is required. If the existence of morality is not so evident, as with Nietzsche and currently fashionable nihilism, then there seems to be nothing left to motivate Kant's concern with transcendent objects.

Major Works

date

age

Thoughts on the True Estimation of
Living Forces

1746

22

On Fire [Doctoral Dissertation]

1755

31

A New Explanation of the First
Principles of Metaphysical Knowledge[Habilitation]

1755

31

General Natural History andTheory of the Heavens

1755

31

Physical Monadology

1756

32

New Theory of Motion and Rest

1758

34

Some Experimental Reflections about Optimism

1759

35

The False Subtlety of the FourSyllogistic Figures Demonstrated

1762

38

Enquiry into the Clarity of the Principlesof Natural Theology and Morality

1762, 1764

38

On the Only Possible Argument forProving the Existence of God

1763

39

Attempt to Introduce the Concept ofNegative Quantitites into Philosophy

1763

39

Observations on the Feeling of theBeautiful and Sublime

1764

40

Dreams of a Visionary, Explained byDreams of Metaphysics

1766

42

The First Ground of the Distinction ofRegions in Space

1768

44

On the Form and Principles of theSensible and the Intelligible World
[Inaugural Dissertation]

1770

46

Critique of Pure Reason

1781, 1787

57

Prolegomena to AnyFuture Metaphysics

1783

59

Idea for a Universal History

1784

60

What is Enlightenment?

1784

60

Foundations of the Metaphysicsof Morals

1785

61

Metaphysical Foundations ofNatural Science

1786

62

Conjectural Beginningof Human History

1786

62

Critique of Practical Reason

1788

64

Critique of Judgment

1790, 1793

66

Religion Within the Limitsof Reason Alone

1793, 1794

69

The End of All Things

1794

70

Perpetual Peace

1795, 1796

71

The Metaphysics of Morals

1797,1798-1803

73

The Strife of the Faculties

1798

74

Anthropology from aPragmatic Point of View

1798

74

Logic

1800

76

But something that Kant overlooks is the Platonic overtone of his own famous statement. The "starry heavens" are especially striking, even for Kant, because they are beautiful. Most people see them, not as factual objects of science, but as things of awe, wonder, mystery, and beauty. Unfortunately, the mature Kant does not have the aesthetic realism of Plato and Schopenhauer, or of the younger Kant himself (in the Observations on the Feeling of the Beautiful and Sublime, 1764). To Plato, the beauty of things is a clue to the transcendent; but the mature Kant decided that only morality played that part. This only reinforces Kant's moralism and weakens his overall theory of value, let alone the metaphysics into which that fits.

The hope of fixing the loose ends of transcendental idealism, and of giving morality itself a credible realistic basis, lies back in the consideration of empirical realism. The unresolved paradox of a "realism" that was also a phenomenalism is the root of the greater difficulties considered above and below. If objects are immanent in experience but independent in their existence, then clearly there is a transcendent aspect to them, however that is construed. God, freedom, and immortality are not actually essential to that, and Schopenhauer did not believe in any of them; but Schopenhauer also overlooked Kant's analysis of "conditioned" versus "unconditioned" objects. Even a physical object, the universe, passes beyond experience and generates metaphysical paradoxes (the Antinomy of space and time), in so far as it is, in its entirety, an unconditioned whole. This is really just what Kant's Ideas are all about. All these matters in Kant's thought are therefore still open to clarification and development, as Fries and Schopenhauer attempted immediately, and as considered elsewhere in these pages.

Despite, but also because of, the paradoxes of his thought, much of philosophy in the Twentieth Century has been ill conceived knock-offs of Kant's theory. The idea that the mind produces the world it knows conspicuously turns up in Wittgenstein's theory of language and now with tedious, endless repetition in "post-modern" theories that see all reality as "socially constructed" on the basis of no more than "power" relationships (ultimately derived from the Marxist notion of ideological "superstructures" to class and economic relations). These all produce a fundamental paradox that was avoided by Kant, for they are all relativistic and subjectivist denials that knowledge even exists, which nevertheless maintain that this circumstance is a fact that can be known and demonstrated with some certainty -- though the "edifying" version of this recognizes the paradox by not trying such a demonstration, while still expecting us to accept the conclusion (!?). Thus, Wittgenstein sees all reality as created by particular languages, even though one might think this would imply that truths about language would be created by particular languages also. And since common sense expressed in most historical languages has actually affirmed that the world exists independently of what we say or think about it, this should mean that it does. Kant, of course, does not see the process of synthesis producing anything relativistic or subjectivist: the realism of phenomena is fully meant. The knock-offs of Kant are rarely realistic.

While the knock-offs occupy fashionable opinion, basic misconceptions about Kantian theory are casually perpetuated. For instance, a defining characteristic of Kantian philosophy is that synthetic a priori propositions are not self-evident and can be denied without contradiction. What makes them true a priori is that they have a cognitive ground which is not in empirical intuition (i.e. perception). Although it is often claimed, as by the great French mathematician Poincaré, that the existence of non-Euclidean geometry refutes Kant's philosophy of geometry, in fact Kant's view of the nature of the axioms of geometry as synthetic a priori propositions means that Kant could have predicted the existence of non-Euclidean geometry. This should be obvious given any clear understanding of the meaning of "synthetic." Only Leonard Nelson fully appreciated this circumstance. The question of geometry in Kant is addressed in "The Ontology and Cosmology of Non-Euclidean Geometry."

The "Inaugural Dissertation" that commemorated his appointment was the first real step towards the characteristic doctrines of the Critical Philosophy. Working that out, and writing the Critique of Pure Reason, still hampered by heavy teaching obligations, then took more than ten years. That book's publication in 1781 put Kant, at age 57, on the doorstep of a vast philosophical project, whose details he had already planned, but whose completion his age and health -- he was never a very robust man -- might well frustrate. His concern that he might actually die before finishing his work, in an age when sudden death was an all too familiar phenomenon, led him to concentrate his efforts with a discipline that has led to caricatures of him ever since -- his clock-like appearance for his daily constitutional, on what then became the "Philosopher's Walk" in Königsberg, is usually seen as evidence of habits mechanical to an absurd extent, rather than the caution and discipline of a frail and aging soul desperate to finish his life's work. His previous custom of dining out and enjoying conversation with his friends was sacrificed in the race against death. What his life had been like we learn from Ernst Cassirer:

"Thus," [F.T.] Rink says, "Kant in his early years spent almost every midday and evening outside his house in social activities, frequently taking part also in a card party and only getting home around midnight. If he was not busy at meals, he ate in the inn at a table sought out by a number of cultured people." Kant gave himself to this mode of life in such an easy and relaxed way that even the most meticulous psychological observer among his intimates was occasionally puzzled about him; in 1764 [Johann Georg] Hamann says that Kant carries in his head a host of greater and lesser works, which he however probably will never finish in the "whirl of social distraction" in which he is now tossed. [Kant's Life and Thought, translated by James Haden, Yale University Press, 1981, pp.51-52]

The race with death, happily, was won, and the key monuments of the Critical Philosophy, including the trilogy of Critiques, were produced. It was declining faculties that finally stilled his pen, before he actually passed away.

Kant's grave has fortunately escaped the destruction that the Soviet occupation visited upon the sights of traditional Königsberg. Kant was born, lived, and died in this city, in East Prussia. It was founded in 1255 by the Teutonic Knights, but named after a crusading companion, King Ottokar II of Bohemia. Today, the names Prussia and Königsberg have both disappeared. After World War II, East Prussia was partitioned between Poland and the Soviet Union, with the northern half held as a part of metropolitan Russia itself. Most native Germans were expelled, and the German name of the capital was replaced with Kaliningrad, commemorating the contemporary President of the Soviet Union. With the fall of the Soviet Union, the "Kaliningrad Oblast" became a detached outliner of the Russian Republic, surrounded by Lithuania and Poland. Most Soviet era cities, like Stalingrad and Leningrad, have reverted to their pre-Communist names. But Kaliningrad has not been renamed, and awkwardly still commemorates the communist Kalinin, since the German name might imply that the district should be returned to Germany. The proposal has been floated to actually name the city after Kant -- i.e. Kantgrad. Since Kant's thought is truly the watershed of modern philosophy, and still the fruitful point of departure for the 21st century, no such monument could be more suggestive, encouraging, and hopeful. Kant, of course, was German himself, so this might not be very much better than the old German name. However, the city was not named after a German, and in origin was not associated with the Kings of Prussia, but after the Slavic King of Bohemia. "Königsberg" thus could simply be translated, without any German overtones. It would then be Korolyagora -- -- in Russian, the "King's Mountain" again. The Russians probably would not be troubled by any Czech claims to it.

I have enjoyed the good fortune to know a philosopher, who was my teacher. In the prime of life he had the happy cheerfulness of a youth, which, so I believe, accompanied him even in grey old age. His forehead, formed for thinking, was the seat of indestructible serenity and peace, the most thought-filled speech flowed from his lips, meriment and wit and humor were at his command, and his lecturing was discourse at its most entertaining. In precisely the spirit with which he examined Leibniz, Wolff, Baumgarten, and Hume and purused the natural laws of the physicists Kepler and Newton, he took up those works of Rousseau which were then appearing, Émile and Héloïse, just as he did every natural discovery known to him, evaluated them and always came back to unprejudiced knowledge of Nature and the moral worth of mankind. The history of nations and peoples, natural science, mathematics, and experience, were the sources from which he enlivened his lecture and converse; nothing worth knowing was indifferent to him; no cabal, no sect, no prejudice, no ambition for fame had the least seductiveness for him in comparison with furthering and elucidating truth. He encouraged and engagingly fostered thinking for oneself; despotism was foreign to his mind. This man, whom I name with the utmost thankfulness, and respect, was Immanuel Kant; his image stands before me to my delight. [Johann Gottfried Herder, Letters on the Advacement of Humanity, letter 79, quoted by Cassirer, op cit., p. 84]

The danger of the "alone" in Kant's statement at A92 is the temptation to disregard the independence of existence and things-in-themselves. If we do that, and imagine that representation effects the existence of its objects, but then we are aware that this process is not under the control of our will or individual imagination, the solution might be to postulate a meta-consciousness, a mind itself possessing intellectual intuition, of which we are merely a part. This is rather like what we find in Spinoza, and, more significantly, in Hegel. Kant's "alone" is thus a kind of aneurysm, whose failure can produce a hemorrhage of Absolute Idealism. The context and cautions that Kant provides should protect us from that, but he does create a weakness.

Kant's most striking early contribution to knowledge, however, was his General Natural History and Theory of the Heavens (Allgemeine Naturgeschichte und Theorie des Himmels, 1755). Kant had two noteworthy theories in physics and astronomy. One was the "Nebular Hypothesis" of planetary formation. Kant reasoned that diffuse nebulae, dim clouds of dust and gas that were only first being well observed in his lifetime, would collapse under the force of gravity. As they did, they could begin spinning and would then spin out into a disk. From these spinning disks stars and planets would condense. Unlike the greatest of earlier German philosophers, Leibniz, Kant was not himself much of a mathematician, so the theory was not given a mathematical form until the great French mathematician Pierre-Simon Laplace (1749-1827) did so in 1796. Although there was still argument in my childhood about the formation of planets, it now seems to be generally accepted that both stars and planets condense out of nebulae and collapsed, spinning disks of dust and gas. There are stellar "nurseries" that can be examined in places like the Orion Nebula. Kant was right. The principal addition to Kant's theory may be that diffuse nebulae are now believed to begin collapsing and spinning because of shock waves from supernovae explosions, which clear voids in nebulae and concentrate material at the edges. Unfortunately, some astronomy textbooks refer to the Nebular Hypothesis as the theory of Laplace alone, instead of the Kant-Laplace theory, and do not give Kant proper credit.

Kant's second theory was also about nebulae, of a different kind. Along with bright and dark diffuse nebulae and planetary nebulae (which have nothing to do with planets), there are spiral nebulae. In Kant's day, I don't believe that the telescopes could resolve these as spirals. But as "nebulous stars," die neblichten Sterne, Kant did distinguish the species, quoting Pierre-Louis Moreau de Maupertuis (1698–1759), as their presenting "the figure of ellipses more or less open [mehr oder weniger offene Ellipsen]," [Immanuel Kant, Universal Natural History and Theory of the Heavens, translated by W. Hastie, Introduction by Milton K. Munitz, Ann Arbor Paperbacks, University of Michigan Press, 1969, p.62; in German: Immanuel Kant, Vorkritische Schriften bis 1768, 1, Werkausgabe Band 1, edited by Wilhelm Weischedel, Suhrkamp, 1960, 1977, p.265, A13].

Laplace believed that these elliptical nebulae were actually the spinning disks of the Nebular Hypothesis. Kant had a different idea. In 1750 Thomas Wright had suggested that the Milky Way, the Galaxy, was a vast spinning disk itself, consisting of stars and everything else, and that the earth was part of this system. Kant had read a report of this theory, and his use of it actually first brought it to general attention. An observational confirmation of it came from the great astronomer William Herschel in 1785. Kant's idea was that the dim, tiny nebulae were themselves external galaxies, "island universes" independent of the Milky Way. He says:

It is far more natural and conceivable to regard them as being not such enormous single stars but systems of many [stars], whose distance presents them in such a narrow space that the light which is individually imperceptible from each of them, reaches us, on account of their immense multitude, in a uniform pale glimmer. Their analogy with the stellar system in which we find ourselves, their shape, which is just what it ought to be according to our theory, the feebleness of their light which demands a presupposed infinite distance: all this is in perfect harmony with the view that these elliptical figures are just [island] universes and, so to speak, Milky Ways, like those whose constitution we have just unfolded. [op. cit., p.63, boldface added]

There was really no evidence for this. It was just a guess. Nevertheless, it launched a great debate that lasted all the way until 1924. Astronomers were either Laplaceans or Kantians. Although Kant is said to have introduced the term "island universes," I do not see "island" in his text, just "universes," Weltordnungen. Nevertheless, the expression became associated with his theory.

Thus, as late as 26 April 1920, there was a formal debate over the issue between Harlow Shapley (the Laplacean) and H.D. Curtis (the Kantian) at the National Academy of Sciences. The matter was not settled by the debate but by Edwin Hubble (1889-1953) in 1923-1924, using the recently completed Mount Wilson 100 inch telescope, in the San Gabriel Mountains above Pasadena, California (the mirror was hauled up the mountain by mules) -- visible from the San Fernando Valley. Hubble was able to identify Cepheid variable stars in nearby spiral nebulae -- initially the Great Spiral Nebula in Andromeda, whose full extent covers three degrees of arc in the sky (six times the diameter of the sun or moon), although only the much smaller core is visible to the naked eye -- actually, the most distance object visible to the naked eye, at 2.38 million Light Years. With this kind of variable star, their period of variation is proportional to their absolute brightness. With their absolute brightness (M), compared to the apparent brightness (m), Hubble would know their absolute distance (m - M = 5 log (r/10), where r is in parsecs). They were far, far further away than the stars of the Milky Way Galaxy. They were in external galaxies. Kant was right.

Hubble's sensational results were presented to a meeting of the American Astronomical Union in December 1924. Now, since it was just a guess, how much credit can we give to Kant? A fair amount, since many great ideas in science begin as guesses, sometimes with little or contrary evidence behind them (as was the case with Copernicus, come to think of it). More importantly, if we ask who the first person was to conceive the form of the universe as we now see it, filled with "billions and billions" of galaxies (as Carl Sagan liked to say), the answer is just: Immanuel Kant, a man who never left East Prussia and who never saw a mountain (although he described them vividly).

Now, not only is it rare to see Kant given credit for his theory, but positive falsehoods can be found in public discourse. Thus, an episode of the History Channel program The Universe, "Beyond the Big Bang" [2007], credited Hubble with being the first person to conceive as well as prove that spiral nebulae are external galaxies, completely ignoring Kant and the long history of the controversy that culminated in the debate between Shapley and Curtis -- which, of course, is not mentioned. Nor is this shocking carelessness and distortion just the fault of the writers of the narrative (they often cannot be trusted on these shows), but we see the assertion seconded by featured talking-head scientists, like Michio Kaku.

We see similar falsehoods, also seconded by Michio Kaku, on the recent Science Channel show, How the Universe Works, "Alien Galaxies" [2010]. The narrator begins the show by saying,

Just a century ago, we thought that the Milky Way was all there was. Scientists called it our 'island universe.' For them no other galaxies existed. Then in 1924, astronomer Edwin Hubble changed all that.

I begin to wonder if Kaku himself is behind the promotion of this distortion. And it is a low blow to use the Kantian term, "island universe," for the very theory, that the Milky Way is the only galaxy, that Kant was contradicting.

Is this problem the result of simple ignorance, or of a positive bias against giving a mere philosopher a significant place in the history of science? There was certainly neither ignorance nor bias with the great UCLA astronomer George O. Abell (1927-1983). Abell will be long remembered for the catalogue he compiled, using the Palomar telescope, of clusters of galaxies, which now are identified by their "Abell" number. Yet Abell gave full credit to Kant in his astronomy textbook, The Realm of the Universe [Hold, Rinehart and Winston, 1976, pp.327-329 -- continued after his death, Abell, G.O., Wolff, S.C., and Morrison, D., Realm of the Universe, Saunders College Publishing, 5th edition, 1994]. Abell quotes Kant and inserts "island" in brackets into the text, just as I have done above.

Since the writers of textbooks tend to look at others in their field, and since scientists like Kaku can be expected to have seen some astronomy textbook in the course of their education, if not Abell's own, that could be informed with Abell's knowledge, it hard to imagine that they simply don't know about the history of the theory of external galaxies. It is shocking to see them endorsing the distortion perpetuated in something like "Beyond the Big Bang" (which, of course, also perpetuates the calumny that geocentric astronomers were just bigoted fools) or "Alien Galaxies." Science education is bad enough in the United States without the History Channel and the Science Channel joining in with gratuitous misrepresentations.

Except for outright Skeptics, Aristotle's solution to the Problem of First Principles, that such propositions are known to be true because they are self-evident, endured well into Modern Philosophy. Then, when all the Rationalists, like Descartes, Spinoza, and Leibniz, appealed to self-evidence and all came up with radically different theories, it should have become clear that this was not a good enough procedure to adjudicate the conflicting claims. This awkward situation was then blown apart by Hume, under whose skeptical examination, reviving the critique of al-Ghazâlî, even the principle of causality crumbled.

The peculiarity of Kant's approach, from an Aristotelian (or Friesian) point of view, is not idiosyncratic. Kant approaches the matter as he does because he is responding to Hume, and one of Hume's initial challenges is about the origin of "ideas." While the Problem of First Principles is about the justification of propositions, Hume's Empiricist approach goes back to asking about the legitimacy of the very concepts, of which the propositions are constituted, in the first place. The Rationalists never worried too much about that. For Descartes, any notion that could be conceived "clearly and distinctly" could be used without hesitation or doubt, a procedure familiar and unobjectionable in mathematics. It was the Empiricists who started demanding certificates of authenticity, since they wanted to trace all "ideas" back to experience. Locke was not aware, so much as Berkeley and Hume, that not everything familiar from traditional philosophy (or even mathematics) was going to be so traceable; and Berkeley's pious rejection of "material substance" lit a skeptical fuse whose detonation would shake much of subsequent philosophy through Hume, thanks in great measure to Kant's appreciation of the importance of the issue.

Thus, Kant begins, like Hume, asking about the legitimacy of concepts. However, the traditional Problem has already insensibly been brought up; for in his critique of the concept of cause and effect, Hume did question the principle of causality, a proposition, and the way in which he expressed the defect of such a principle uncovered a point to Kant, which he dealt with back in the Introduction to the Critique, not in the "Transcendental Logic" at all. Hume had decided that the lack of certainty for cause and effect was because of the nature of the relationship of the two events, or of the subject and the predicate, in a proposition. In An Enquiry Concerning Human Understanding, Hume made a distinction about how subject and predicate could be related:

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain [note: these are Locke's categories]. That the square of the hypothenuse is equal to the square of the two sides, is a proposition which expresses a relation between these figures. That three times five is equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.

Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind. [Enquiries, Selby-Bigge edition, Oxford, 1902, 1972, pp.25-26]

Both paragraphs warrant quoting in full. The first now would seem properly more a matter of embarrassment than anything else. Whatever Hume expected from intuition or demonstration, it would be hard to find a mathematician today who would agree that "the truths demonstrated by Euclid would for ever retain their certainty and evidence." If Hume's fame rests on this point, there would be little to recommend it. The second paragraph, however, redeems the impression by giving us a logical criterion to distinguish between truths that are "relations of ideas" and those that are "matters of fact": A matter of fact can be denied without contradiction.

This was the immediate inspiration to Kant, who can have asked himself how something "demonstratively false" would "imply a contradiction." A contradiction means something of the form "A and not-A." If a proposition expressing a matter of fact can be denied without contradiction, then the subject and the predicate of such a proposition cannot contain anything in common, otherwise the item would turn up posited in the subject but negated in the predicate of the denial. On the other hand, a proposition that cannot be denied without contradiction must contain something in the predicate that is already in the subject, so that the item does turn up posited in the subject but negated in the predicate of the denial. This struck Kant as important enough that, like Hume, he founded a whole critique on it, and also produced some more convenient and expressive terminology. Propositions true by "relations of ideas" are now analytic ("taking apart"), while propositions not so founded are synthetic ("putting together").

This clarified distinction Kant could then turn on Hume's own examples of "relations of ideas." Can geometry be denied without contradiction? Kant did not see that the predicates of the axioms of geometry contained any meaning already expressed in the subjects. They were synthetic. They could be denied without contradiction. Geometry would thus not have an intuitive self-evidence or demonstrative certainty that Hume claimed for it. Kant still thought that Euclid, indeed, would have certainty, but the ground of certainty would have to located elsewhere. Nevertheless, Kant is rarely credited, and Hume rarely faulted, for their views of the logic of the axioms of geometry. If the axioms of Euclid can be denied without contradiction, this means that systems of non-Euclidean geometry are logically possible and can be constructed without contradiction. But it is not uncommon to see the claim that Kant actually denied this, and it is Kant, not Hume, who is typically belabored for implicitly prohibiting the development of non-Euclidean systems. This distortion can only come from confusion and bias, a confusion about the meaning of "synthetic" (even in Hume's corresponding category), and a bias that the Analytic tradition has for British Empiricism, by which the glaring falsehood of Hume's statements is ignored and Kant's true and significant discovery misrepresented. This curious and reprehensible turn is considered in detail elsewhere.

Kant, as it happens, also did not see how arithmetic could be analytic. In his own example of "7 + 5 = 12" (p. B-15), if "7 + 5" is understood as the subject, and "12" as the predicate, then the concept or meaning of "12" does not occur in the subject. This was rather harder to swallow than the point about geometry, for it seems rather "intuitively" certain that "7 + 5 = 12" cannot be denied without contradiction. Kant must have missed something. Hope for demonstrating the analytic nature of arithmetic came with the development of propositional logic, since a proposition like "P or not P" clearly cannot be denied without contradiction, but it is not in a subject-predicate form. Still, "P or not P" is still clearly about two identical things, the P's, and "7 + 5 = 12" is more complicated than this. But, if "7 + 5 = 12" could be derived directly from logic, without substantive axioms like in geometry, then its analytic nature would be certain. In their Principia Mathematica (1910-1913), Russell and Whitehead and, in the Tractatus, Wittgenstein thought that they could indeed derive arithmetic from logic. Their demonstrations, however, were flawed, and it turned out that substantive axioms were necessary, just like in geometry. The axioms are now those of axiomatic Set Theory, and it is Set Theory that concerns the foundations of arithmetic. Kant turned out to be right again, though, curiously, he is again rarely credited for this.

Kant's discovery, however, can be trivialized if it turns out that there are simply no analytic propositions at all. This task was undertaken by Willard Van Orman Quine ("Two Dogmas of Empiricism," 1950). The approach, simply enough, was Nominalistic. If we say that "red is a color" is an analytic proposition, where is "color" in "red"? I don't see it. If we say that the meaning "color" is in the meaning of "red," where are these "meaning" things? I don't see them. Thus, if language consists of words but not abstract meanings, then we don't have to worry about one meaning containing another. "Red is a color" is just a convention of our language, which is even what we can say about "P or not P." Besides the general failings of Nominalism, Quine's particular critique is well refuted by Jerrold Katz.

In Kant there is little left in the category of "analytic." Definitions and truths of logic are going to be about it; and the definitions themselves will be suspect when the concepts defined may or may not be legitimate. The meaning within a concept must also in some sense be "put together," and the ground of this will raise the same questions as the ground of synthetic propositions. Thus, Saul Kripke began to speak of "analytic a posteriori" propositions, when the meanings in the subject are themselves united on only a posteriori grounds, i.e. the basis of experience. Indeed, dictionary definitions of natural language words are prima facie of conventional usage, e.g. how a pot is different from a pan, and the meaning of any words can be simply stipulated for some appropriate purpose, e.g. a "designated hitter" can go to bat for some particular member of a baseball team (usually the pitcher), without otherwise replacing him in other play. Thus, a big fight over the existence of analytic propositions doesn't in the end make that much difference. Synthetic propositions are the key anyway, as they were if Kant wanted to answer Hume's critique of causality.

For, indeed, outside of an axiomatized logic itself, the First Principles of Demonstration will be synthetic. However Kant can explain the truth of non-empirical synthetic propositions, i.e. those that are a priori instead of a posteriori, that will be his answer to the Problem of First Principles. They are clearly now, after Hume, not going to be self-evident. Yet Hume himself is often poorly understood. While it is common to say that Hume denied the existence of synthetic a priori propositions, there is some question about whether he actually does. He says that the relationship of cause and effect is not discovered or known by any reasonings a priori, but that is not the same thing. A synthetic a priori proposition is not known from any reasonings. In fact, Hume does not see that the relationship of cause and effect is discovered or known from anything, since it is not justified by experience, in which there is no necessary connection between cause and effect, and there is in fact nothing in the cause to even suggest the effect, much less that the effect must follow. Hume's famous explanation was a psychological one, that we become accustomed to the association of certain events ("causes") with others ("effects"); but this, obviously, carries no weight whatsoever about the nature of things, which is what makes Hume, very properly, a Skeptic.

At the same time, Hume had no doubts whatsoever of the necessity of cause and effect. This is where he is commonly misrepresented. People assume that because he was a Skeptic, then he must have thought it possible for causes to occur without effects, i.e. for the principle of causality to be contradicted in actuality. He never had any such expectation, and in fact he ruled out a priori, not only miracles, but also chance and free will just because they would violate (a very deterministic) causality. Confusion over this occurs because people do not appreciate that Hume as an "Academic" Skeptic, holding that lack of knowledge (the meaning of "Skepticism") does not rule out "reasonable" beliefs. Causality is a "reasonable" belief because, as Hume says, "All reasonings concerning matter of fact seem to be founded on the relation of Cause and Effect" [Enquiry, op. cit., p. 26]. So without it, we would have no basis of reasoning in daily life. Thus, Hume says:

Nor need we fear that this philosophy, while it endeavors to limit our enquiries to common life, should ever undermine the reasonings of common life, and carry its doubts so far as to destroy all action, as well as speculation. Nature will always maintain her rights, and prevail in the end over any abstract reasoning whatsoever. Though we should conclude, for instance, as in the foregoing section, that, in all reasonings from experience, there is a step taken by the mind which is not supported by any argument or process of the understanding [i.e. from cause to effect]; there is no danger that these reasonings, on which almost all knowledge depends, will ever be affected by such a discovery. [ibid., p. 41]

Kant therefore understood that Hume's problem was not with the quid facti, that there were causes and effects, and necessary connection, but with the quid juris, the epistemic justification of the principle. While some philosophers spent much of the 20th Century congratulating Hume for having discovered that causality might not exist, they never seem to have noticed that he explicitly denied having done anything of the sort. Kant already knew the type, who "were ever taking for granted that which he doubted, and demonstrating with zeal and often with impudence that which he never thought of doubting..." [Prolegomena to Any Future Metaphysics, p. 259, Lewis White Beck translations, Bobbs-Merrill, 1950, p.6].

Kant's solution to the quid juris in the Critique of Pure Reason was the argument of the "Transcendental Deduction" (in the "Analytic of Concepts") that concepts like causality are "conditions of the possibility of experience," because they are the rules by which perception and experience are united into a single consciousness, through a mental activity called "synthesis." Once the existence of consciousness is conceded (which not everyone, e.g. behaviorists, might be willing to do), then whatever is necessary for the existence of consciousness must be conceded.

This is a strong argument and, decisive or not, is heuristically of great value, especially when we untangle it from the earlier views of perception in the Critique. However, it suffers from a couple of serious drawbacks. One is that, like Hume's own explanation, it is a psychological approach that does not necessarily tell us anything about objects, i.e. consciousness may be united in a way that is irrelevant to external things. Kant seemed to recognize this himself when he said that none of this gives us any knowledge of things-in-themselves. This problem was never properly sorted out by Kant, and is considered independently in "Ontological Undecidabilty".

The second drawback of Kant's argument is that it would only work, indeed, for the "conditions of the possibility of experience," and not for any other matters which might seem to involve synthetic a priori propositions. Hume himself was just as concerned about morality as about causality, and found himself in the same Skeptical position in both matters. The only comparable thing that Kant can do for morality, however, would be to employ a principle of the "conditions of the possibility of morality." But this would require conceding that morality exists, which is something that a very large number of people in the 20th century, far beyond behaviorists, would not be willing to do. Nor does it make one a Kantian merely to vaguely appeal to human "rationality" (e.g. John Rawls) as a basis for morality, since this really just begs the question of justification -- besides violating Hume's famous observation that propositions of obligation ("ought," imperatives) cannot be logically derived from propositions of fact ("is," indicatives).

Keeping in mind that First Principles cannot be proven, and that synthetic propositions can be denied without contradiction, the conspicuous historical alternatives seem to be to deny one or the other. Hegel denied the first, by taking the equivalent of Kant's Transcendental Deduction as itself a part of metaphysics and a proof, by means of novel principles of "dialectical" logic, of moral and metaphysical truths. To an extent, Hegel may also have denied the second, as Leibniz certainly did, treating any moral or metaphysical truth as analytic, if only from the point of view of divine omniscience. Either such move, however, cannot escape the original embarrassments of Rationalism, or avoid the devastation inflicted by the criticisms made by Hume and Kant.

Less conspicuous historically was Jakob Fries, who could accept the proper meanings of "First Principle" and of synthetic propositions. The Friesian theories of deduction and of non-intuitive immediate knowledge make it possible to preserve the advances of Hume and Kant without falling back into Rationalism or heading for the Nihilism (so different from Hume's Skepticism), relativism, scientism, pragmatism, etc., so conspicuous in the 20th century. Later, Karl Popper proposed a special solution for the Problem in that science, by using falsification, does not need to worry about a positive justification of First Principles at all. This enables scientific progress to heedlessly continue, as it has, regardless of the status of any philosophical solution.

Thus, Kant gave us the real elements of the solution of the Problem of First Principles, even though he could not complete and seal the matter himself. Indeed, no one can hope to do that, even as new elements and new understanding of the solution emerge over time.

If we try to construct a square of opposition using Kant's two distinctions, we have some trouble. A strictly constructed square of opposition would look like the one at right. "Transcendental" (e) is the negation of "empirical" (e), and "idealism" (r) is the negation of "realism" (r). The structure we get, however, does not work for Kant's theory. Transcendental idealism and empirical realism would be contradictories and so cannot both be true, as Kant requires. Similarly, transcendental realism and empirical idealism are also contradictories and so cannot both be false, as Kant requires. The features of the square of opposition that we would expect Kant's theory to conform to would be that "contraries," the two upper members, are both false, while the "subcontraries," the two lower members, are both true.

If we want such a square of opposition, it will have to be rearranged without regard for the strict logical properties of the terms. We can save the distinctions and do that by recalling that opposites contradict each other only when applied to the same objects. Black coal and white snow are not contradictions. Kantian realism and Kantian idealism are thus reconciled by a distinction, that between phenomena and things-in-themselves. The former applies to the former, and the latter to the latter.

We can then produce a square like the one at right, which allows for the traditional truth values. In this version the definition of "transcendental idealism" has actually been left out. Kant's position, although terminologically embracing the two lower members, is really well defined by only one of them, empirical realism. However, saying that the objects of knowledge are immanent in experience and independent of our existence involves a paradox. How can something be independent in existence and yet dependent or immanent in our experience, our representation?

...the representation alone must make the object possible... ...representation in itself does not produce its object in so far as existence is concerned... [A 92]

The common sense, direct acquaintance with objects, part of this is what Kant appears to mean by his empirical realism, while the paradoxical, "in me but not of me," metaphysics is what he means by "transcendental idealism." This is the paradox addressed by Schopenhauer and by "Ontological Undecidability."

However, using the strict definitions, "transcendental idealism" means something else, as reproduced in the entry at left. If "transcendental" means, epistemically, "independent of experience," but "idealism" means, ontologically, "dependent on subjective (my) existence," then "transcendental idealism" would have to mean knowledge of objects that are dependent on my existence but independent of my experience. This seems to be, not just a paradox, but an out and out contradiction, since if something exists as an epiphenomenon of myself, it hardly seems like it could be independent of my experience. Berkeley's principle was "to be is to be perceived," but this kind of "transcendental idealism" would require that something is because of my existence but then is not perceived. This might work on the basis of Spinoza's metaphysics, where my existence is God's existence, but God's knowledge far transcends mine. Nevertheless, since anything is God, God is part of my experience after all.

What this peculiar meaning of "transcendental idealism" reveals are the loosest ends of Kant's thought. The terminology of "transcendental," "empirical," "realism," and "idealism" does not seem well ordered for Kant's purposes, in part because those purposes are unsettled. The contradiction of the strict rendering of "transcendental idealism" might be resolved if we say that there is simply no knowledge in this case, which is pretty much what Kant says about things-in-themselves -- the soul certainly depends on my existence but is not part of my experience because I don't have any knowledge of it. But then Kant doesn't want to go all the way with that. Morality doesn't fit into empirical reality, but then maybe that isn't too bad, since morality is really "regulative" rather than "constitutive" (of metaphysical entities). What is bad are "God, freedom, and immortality," which totally upset the applecart. If there are such things, they are about transcendent objects which, at least in one case, are independent of my existence. If they are only objects of "faith," we want to know how that is motivated; and if they are motivated as necessary conditions of the Moral Law, then it seems like they would be as much matters of knowledge as the necessary conditions of experience, i.e. causality, substance, etc.

My view is that the way out of this is through Friesian epistemology. Nevertheless, Kant's theory, as an approximation, is superior to any that have come since -- let alone the dismal exercises in nihilism, scientism, and scholasticism that are now so popular.

Update, 2010

Since I have not been happy with the logic of Kant's terminology concerning transcendental idealism and empirical realism, I have been trying to think of different ways to restate it. This diagram is another square of opposition, but the truth values are not determined by the properties of the square. Instead, we are looking at certain concepts, which themselves are no more than features of particular theories. While the concepts thus obey the principles of the square, they leave the truth of the theories underdetermined, which means that the truth or falsehood of the theories is a separate issue and is not reflected in the logic of the square.

The concepts in the square are "subject" ("s") and "object" ("o"); and what they reflect is the idea whether the existence of subject and object transcend the contents of consciousness (appearances, phenomena). Thus, in Transcendental Idealism, the existence of both subject and object transcends appearances. This is the right idea, and the true theory, in Kantian terms.

The opposite of this ("so") is that the existence of neither subject nor object transcends appearances, i.e. phenomenal reality is all that there is and there are no things-in-themselves. This is actually the form of Hegel's metaphysics. Since the terms of this diagram are purely metaphysical and not epistemic, calling Hegel's theory "empirical realism" has a very different meaning from the way Kant uses it. It is also now false, with all the evil consequences, such as judicial positivism, of Hegel's philosophy.

If the existence of the subject transcends appearances, but that of the object does not ("so"), we find something like Berkeley's metaphysics, where matter does not exist, and objects have no independent reality, but there is a soul. We can call this, as Kant does, "empirical idealism."

Finally, if the existence of the object transcends appearances, but that of the subject does not ("so"), we have a take on the metaphysics of Descartes. Now, at first blush, this characterization looks paradoxical and wrong for Descartes, who, after all, famously posited the existence of the soul over and above that of matter. However, Descartes saw the existence of the soul in a certain way: it was part of the external order of objects in space and thus possessed a location in relation to matter and was supposed to physically interact with it. This is the source of a veritable eruption of paradoxes and embarrasssments in the Cartesian system. Thus, while the essence of the Cartesian soul is subjectivity, it is part of what ontologically is an external order of things.

We therefore have a new way to think about these distinctions. "Internalism" is the transcendence of the subject from appearances; and "externalism" is the transcendence of the object from appearances. In Descartes, the transcendence of the subject is misconceived in externalist terms. This produces something that is one of the major paradoxes of Cartesian philosophy: the whole mess looks more sensible than the more logically coherent constructions of Spinoza and Leibniz, let alone Hegel. What we do get in Hegel, then, is the rejection of both internal and external transcendence. We might characterize the result as an "immanentalist" phenomenalism.

Kant's theory, as a result, preserves both internal and external transcendence. And it does so without reducing one to the other. This is a considerable achievement, since the structure looks unnatural and unstable. We want to know, is existence really internal? or external? I have expressed precisely this balance, and our inability to reduce internal or external to the other, as Ontological Undecidablity.

Wills, indeed, represents a Hegelian movement in American political thought, going back to John Dewey ("Things gain meaning by being used in a shared experience or joint action") and earlier, that exalts the collective and the state and sees the imperfections of man as something that can be overcome with the perfection of the government. Kant and Madison, aware that a government is something "which is to be administered by men over men," would find this movement perfectly senseless and dangerous. The idea that politicians and bureaucrats are disinterested servants, to whose wisdom and goodness absolute power can safely be entrusted, is a notion so preposterous that most persons of adult perspicacity see through it easily -- even if they do not know about rent seeking and Public Choice economics. Why an intellectual like Garry Wills is deceived may be due to an effect familiar since Plato: the tempting answer to all politics that the only real problem is that the wrong people are in charge, while the right people, of course, would be someone like themselves (e.g. Plato, Wills, etc.). This has tempted many of the naive and self-deceived, not only into folly, but into evil.

The statement by Madison is so appropriately coupled with Kant because Kant believed that moral perfection was only possible with an "angelic will," a will in which the imperative of rational morality is not obstructed or compromised by irrational influences. Where these irrational influences come from is clear enough. As sensation contributes the material for synthesis, perception, and empirical knowledge, it also contributes the sensual and self-interested temptations that conflict with rational duty. In short, the phenomenal world is the place of the Fall, where our nature is so compromised that the moral perfection of God or the angels is impossible. This seems to me the most Christian feature of Kant's thought, or perhaps the only Christian feature. However, were Kant a Christian, he would know that Fallen human nature can be redeemed through Jesus Christ. But we see no such thing allowed. Instead, it is an important part of Kant's argument for immortality as a Postulate of Practical Reason that the absolute command of the Categorical Imperative, to be perfect, can only be met if we are given infinite time, i.e. immortality, to meet it. Come to think of it, the requirement of perfection has a Biblical basis also: "Be ye therefore perfect, even as your Father which is in heaven is perfect" [Matthew 5:48]. My understanding is that eternal life in Christian thought is a reward for faith and for repentance. For Kant, however, eternal life is simply the way to deal with our hopeless imperfection. Repentance and redemption don't seem to figure in at all, though Kant is not unaware of what he formulates as his own question, "What can we hope?" An eternity of futile moral improvement sounds more Sisyphean than hopeful.

The imperfection of the world contradicts a principle that is the opposite of the Kantian, namely moral heteronomy, that the standard, the paradigm, and the authority of the right and the good stand outside of us in the world. Where the world can contain no such thing, then our knowledge of the standard of the good comes from within, a matter of Kantian autonomy. Heteronomy is what we see in Aristotle and Hegel, with the former because virtue is a matter of achieving good habits by imitation, with the latter because, where the "real is rational," the state embodies that rationality. For Kant, the rationality of the world is evident in science, but the rationality of morality tends to be contradicted, not affirmed, by the world. We are thus in the world, but not of it, as Plato might have been the first to say. Autonomy is then a principle of conscience and of political freedom. There is nothing in the world that can claim absolute obedience, because there can be nothing in the world that, by its perfection, can be worthy of such obedience. Knowing how government and the law often actually work, no one could be deceived that any blind obedience is owed to it. As Madison said, "No government, any more than an individual, will long be respected without being truly respectable" [Federalist Paper No. 62].

An imperfect government in an imperfect world of autonomous individuals means that the aims of life are not going to be the business of government. The government is thus not, in Michael Oakeshott's terms, a teleocracy, rule that has some end (telos) in view. It will only be a nomocracy, a government of abstract laws (nomoi) that limit the means of action, regardless of the ends. That is then conformable to a Lockean and Jeffersonian view of government as existing to secure the natural rights, the negative rights as Berlin said, that protect individuals from others. The Kantian moral respect for the will and rational nature of others contrasts with the Hegelian sentiment that "All worth which the human being possesses -- all spiritual reality, he possesses only through the State." To find meaning in something larger than oneself is noble, but this becomes poisonous when the "something larger" is interpreted as only meaning government and the state, to the point where a particular kind of political activism becomes viewed by educators (following Dewey?) as the only moral and enlightened thing. Mussolini's conception of "totalitarianism," after all, was simply that all meaning is found in the "totality," the collective. It is ironic that a favorite leftist accusation against those suspicious of government action is that they don't "care" about other persons -- when their own idea of "care" is the action of something, the government, that always has the sanction of force behind it. The individual uncooperative with the "care" of government is liable to find men with guns breaking into his home. This has happened to people like Peter McWilliams who after becoming gravely ill have discovered that marijuana has medicinal value. The state disapproves; and Peter is dead.

Where Kant goes very wrong is with the notion that the imperfection of the world is simply due to sensation and the sensible nature of our experience. This is pregnant, not just with the moralism that otherwise troubles Kant's ethics, but with the anaesthesia and anhedonia, the denial of the value of art, beauty, and pleasure, to which moralism tends. It is not surprising then that Kant should have moved from the aesthetic realism of his Observations on the Feeling of the Beautiful and Sublime to the doctrine of the Critique of Judgment that aesthetic feeling is subjective and simply a result of a "harmony of the faculties" between perception and morality. We might see this as another Christian characteristic of Kant if we agree with Nietzsche's thesis to any extent that Christianity is anaesthetic. Indeed, an ascetic impulse in any religion or politics will tend to anaesthesia and anhedonia.

Kant's error can be partially corrected by returning to Plato, or advancing to Schopenhauer. With both of them, beauty is the clue, the reflection, or even the "participation" of a different order of reality. It is the very direct presence of something which stands in stark contrast to all other imperfection in the world. Certainly, the world is not perfected thereby, and Schopenhauer would not think of beauty as indicating a separate reality to which we could go. However, all we need is Kant's own famous quote, "Two things fill the mind with ever new and increasing admiration and awe, the oftener and more steadily we reflect on them: the starry heavens above me and the moral law within me." This combines moral autonomy with "starry heavens" (der bestirnte Himmel, "the bestarred heaven") that are, to be sure, objects of scientific knowledge, but also fascinating images of beauty -- that only thing that would draw, indeed, such enthusiasm ("admiration and awe") as we see in the quote. Even a more realistic appreciation of beauty, however, does not quite do the job. Pleasure has never quite recovered from Mediaeval anhedonia. Nevertheless, the smug attitude happy to blame religion for this faces the difficulty that modern political moralism is fully as anhedonic as any religion. The leftists (and conservatives) who fulminate against "consumerism" really mean the pleasures that are fostered by -- in Plato's phrase and theirs -- the "unnecessary desires" created by advertising and modern production. At least Ted Kaczynski, the Unabomber, was willing to give up modern technology (except in the interests of his Terrorism, when he was ready to use airplanes, the postal system, etc.), while I doubt that most critics of "consumerism" are.

So, unfortunately, the bottom line on pleasure may still be Aristotle:

Men erring on the side of deficiency as regards pleasures (hêdonás), and taking less than a proper amount of enjoyment (khaírontes, "enjoying") in them, scarcely occur; such insensibility (anaisthêsía) is not human (anthrôpiké) [Nicomachean Ethics, Book III, xi, 7, Loeb Classical Library, Harvard U. Press, 1926-1982, pp.180-183].

Both religious and political anhedonia are, especially when forcefully imposed on others, "not human." With Kant's "crooked timber," it is hard not to see the crookedness contributed in great measure by the existence of pleasure. Yet pleasure is a good. Like all goods, it may or may not become a moral issue. Nor is moral evil always the result of self-interest, sensuality, or pleasure. The path to hell is paved with good intentions, and in both religion and politics some of the most dangerous and vicious people are the ascetic and the disinterested. Doing good for others sometimes can visit the greatest evils upon them.

Kant's principle thus gives us one way to forestall political utopianism and totalitarianism, but it is also not quite the right idea, and its further implications must be examined carefully.

Kant, of course, had no interest in mysticism, famously pillorying the Swedish spiritualist, Emanuel Swedenborg ("Dreams of a Visionary, Explained by Dreams of Metaphysics," 1766), but it is important to note what mysticism would be in Kantian philosophy. Any kind of mysticism is going to be a kind of immediate knowledge that is an intuitive understanding, i.e. the opposite of a discursive understanding, where an intuitive understanding is immediate and unarticulated, while a discursive understanding is mediate and articulated. There is going to be no intuitive understanding in Kantian philosophy -- i.e. no understanding that stands on its own as knowledge, an understanding that is a ground for substantive truths. An intuitive understanding which is not knowledge is the common and essential experience of insight which is ordinarily and non-technically called "intuition," e.g. "My intuition is that murder is wrong" (in German, Nelson called it Intuition in contrast to Kantian Anschauung). This kind of "intuition" is not evidentiary, i.e. it doesn't prove anything. In Socratic/Platonic terms, it is only opinion. It can only be justified when analyzed, reduced to discursive understanding, and grounded accordingly [note]. Were ordinary "intuitions" evidentiary, and so items of knowledge (Erkenntnisse, cognitions), then this would be "intuitionism," the theory that knowledge is grounded by such intuitions [note]. The self-evidence of Aristotelian first principles is a theory of this kind, with the proviso that intuitive self-evidence follows, rather than precedes, discursive understanding. Other forms of intuitionism may claim intuitive understanding prior to discursive, if the latter is considered even possible.

While mysticism is a form of intuitionism, not all intuitionism is mysticism. The difference, again, will be in the objects. Mysticism is intuitive knowledge of transcendent concrete objects, i.e. not the phenomenal or material concrete objects of ordinary perception. The mystic sees things that are not part of ordinary experience. In Kantian terms, transcendent objects cannot be understood because they cannot be consistently articulated. For Kant, a theory of transcendent objects ("dialectic") generates antinomies. If a Kantian theory allowed for mystical knowledge, it would have to be unanalyzable, unrenderable into a system of discursive understanding of transcendent objects. This is rather like what many mystics say, since they gain knowledge which is ineffable and inexpressible. On the other hand, mystics also claim to intuitively derive knowledge which is analyzable and expressible, although only intuitively justified, since, for instance, al-Ghazzali (1059-1111) finds specific justification of Islâm and its doctrines through mystical insight.

The intuitive apprehension of abstract objects does not rise to the level of mysticism, since abstract objects do not have independent existence -- except when substantialized in Platonism, a theory rarely followed since. Intuitions of abstract objects concern meaning, and in general the ordinary sense of "intuition" (Intuition) applies to this. Such intuitions, when analyzed, are the basis of analytic truths, but whether the meanings apply to existence is a separate question (pace St. Anslem and Descartes), which requires an evidentiary basis. The mystical claim would have to be that an intuitively apprehended abstract object is also intuitively known to apply to existence, in a way, analyzable (as in Anselm's "ontological argument") or unanalyzable, that transcends ordinary perception and experience.

An important distinction in mystical claims will be between objects which are independent and which are identical to the subject of mystical knowledge. This itself is an analyzable characteristic of mystical intuition. In monotheistic religions, God will tend to be seen as independent. This was not an open question, and the Christian mystic always ran the risk that contrary truths learned through mystical intuition might conflict with Orthodoxy -- but the Catholic Church never denied that such an avenue of knowledge existed, as with St. Teresa of Ávila (1515-1582). Other mystics, however, paid the price of their experiences at the stake. In Judaism and Islâm, with looser institutional authority over doctrine, the drift of claims towards extinction of self and identity with God is conspicuous. Some efforts were made in Islâm to suppress this, like the execution of al-H.allâj (in 922), but the precedent was powerful. An artifact of this in Judaism remained with the philosopher Spinoza, whose sense of identity with God is crystal clear, but who cannot properly be considered a mystic, since his God is not transcendent, but immanent, identical with all the objects of perception, and who does not claim intuitive knowledge beyond the minimal Aristotelian claims about first principles. Nevertheless, Spinoza retains a strong mystical affect, the "intellectual love of God," which helps explain the meaning to him of a system that otherwise is rationalistic and seems devoid of religious appeal.

The distinction between independent and identical objects can be seen to overlap Kant's between intellectual and sensible intuition. Only a sensible intuition could relate one to an independent transcendent object, since such a thing clearly cannot be created by one's knowing it. However, if the mystic is identical to the transcendent object, this could allow for an intellectual intuition, depending on the metaphysics of the object. It is possible for God's existence to be presented to him passively, in which case he would have sensible knowledge of himself; or, God may actually create his own existence, like that of anything else, merely by knowing it. This fits Spinoza's principle of a substance, namely God (Spinoza's only substance), being self-caused. There, if the mystic is identical to God, who also creates everything else through intellectual intuition, all mystical knowledge will be of the nature of an intellectual intuition.

This is even simpler in Buddhism, where there are no substances and, at least in some forms of Buddhist philosophy (e.g. Yogacara), all things are clearly created by Mind. In Pure Land Buddhism, an important meditative practice is the visualization of the Pure Land of the Buddha Amitabha. It is always possible to interpret this as unrelated to the independent, or even real, existence of the Pure Land, but the metaphysics clearly allows that the Pure Land is actually created by the act of visualization, since all things are Mind dependent. This would be an intellectual intuition in a strong Kantian sense, and a form of mysticism, with the transcendence of the Pure Land, in which the identity with the mystical object is facilitated by the absence of any substantial independence of things whatsoever. Similarly, the Tibetan "Book of the Dead" urges the deceased to realize that the visions of the hereafter are not independent but created by their own Mind. Thus lies the path to Enlightenment and Salvation.

In light of this examination, we should revisit the charge of mysticism against Rudolf Otto. Since Otto does not claim intuitive knowledge of transcendent objects, he clearly is not a mystic. The natures of transcendent objects, to the extent that they can be theorized at all, are matters of rational Kant-Friesian metaphysics (after the fashion of Kant's "postulates of practical reason," which resolve some antinomies); and Kant-Friesian metaphysics tends to dismiss more substantive doctrine from historic religions (e.g. the Trinity, transsubstantiation, etc.). Otto's famous theory of "numinosity" is about a property, and so an abstraction, whose existence is certified by its presence in the objects of experience, but which in an important way is not a natural property, since it is invisible to science and is unrelated to mundane utility. The numinosity of God is natural to Otto, but his God comes from the Kantian Ideas, besides historic religions, and divine numinosity derives from no more than a phenomenology of such religions.

So is there mysticism? Of course, there actually are mystics, most of whom are clearly sincere and deeply moved or transformed by their experiences. But there is no philosophical mysticism in the sense that philosophy could, as the Neoplatonists believed, certify, verify, and theorize the results of mystical intuitions. Given a Kantian epistemology and metaphysics, no rational or intelligible system can be built from mystical intuitions, analyzable or unanalyzable. This, however, should be no more than what we would expect given the contradictory claims of mystical or dogmatic authorities in world religions. The antinomical choices between mystical intuitions as intellectual or sensible, of independent or identical objects, of a divine substance (personal or impersonal) or ultimate Emptiness, cannot be resolved on the evidence of mystical knowledge, since the knowledge of different mystics confirms each of these and, as Hume would say, the evidence of one tends to refute the evidence of the other. This in itself is one of the most important features of human existence, since it leaves us without any rational certainty that there are transcendent objects at all. The mystic may just be hallucinating (or lying), whether beholding the Virgin Mary or visualizing the Buddha Land. As considered elsewhere, however, this simply leaves us faced with the choices of the right and the good without any confidence in the ulterior considerations of reward and punishment. Behind our veil of ignorance, it is character and benevolence that are proven.

Intuition and Mysticism in Kantian Philosophy, Note 1

Problems of justification are covered elsewhere. In Kant's theory, complications arise over Kant's original, "architectonic," conception of intuition (Anschauung) because, as considered in the main essay on Kant, perception itself comes to be seen (in the Transcendental Deduction) as a product of mental activity. If perception is itself active and intellectual, then the simple distinction between sensible and intellectual intuition, or even between intuition and thought, becomes confused. Friesians like Nelson don't deal with this very well and tend to take over Kant's own naive version of the theory.

However, as is examined in detail in The Origin of Value in a Transcendent Function ("Intuition and the Immanent Object), the immediacy of intuition that is lost when we consider perception to be the result of active mental synthesis returns when we realize that this synthesis is an activity that cannot occur in the conscious mind. Perception is spontaneously produced by a preconscious activity; and even if it is governed by Kant's "pure concepts of the understanding" as rules of synthesis, these concepts do not accompany the results as conceptual or semantic content. Perception can occur without being understood, without particular things being seen, or without a particular recognition determined by the percept -- as in the Gestalt tricks where different things (e.g. faces or candlesticks) can be seen in the same shapes. The difference between conceptual meaning and perceptual object must be maintained, even when the empiricist tabula rasa is rejected and mental processes are allowed into the formation of perception. It is thus possible to continue speaking of intuition pretty much as Kant and the Friesian do, even after taking into account the way that the Transcendental Deduction undermines Kant's original view of intuition. There is also the ontological aspect to this, that the phenomenal objects immanent in perception are undecidably both real/external and subjective/internal.

Intuition and Mysticism in Kantian Philosophy, Note 2

In arguments about mathematics and set theory, "intuitionism" tends to mean something else, which can be very confusing. Mathematical intuitionists don't like mathematical or logical constructions that cannot be visualized (hence, "intuited") and so tend to be wary or disapproving of infinities. Such scruples, however, which may be empiricist in origin, seem to have had little effect on the practice of mathematics and, if taken seriously, would make much of modern mathematics, including non-Euclidean geometry, suspect. While Kant might be said to be a kind of intuitionist in this sense, since he thinks that the axioms of geometry and arithmetic are grounded by visualization, there is nothing to prevent the logical extension of mathematics beyond our capacity for visualization, which in fact is what has occurred. While Kant's mathematics is somewhat intuitionistic in the modern mathematical sense, it is not necessarily intuitionistic in the traditional epistemic sense, since our mathematical "intuitions," e.g. "that looks like a triangle," can be wrong. The Kantian mathematical intuition is much more like perception, an empirical intuition, than it is like a true self-justifying, evidentiary intuition -- a Kantian mathematical intuition, like an empirical intuition, can be misunderstood, while the evidentiary intuition of (epistemic) intuitionism is itself a kind of infallible understanding. To prevent confusion, the mathematical sense of "intuition" and "intuitionism" is not used in the text.

In Modern philosophy there is correspondingly little doubt that knowledge penetrates to the fundaments of reality until we encounter, indeed, the Skepticism of David Hume, who says, about the objects of scientific inquiry, "These ultimate springs and principles are totally shut up from human curiosity and enquiry" [Enquiry Concerning Human Understanding, Shelby-Bigge edition, Oxford, 1902, 1972, p.30]. Now, it was reading Hume, Kant says, that awakened him from his dogmatic slumber. Kant's "Copernican Revolution" then not only reverses the roles of representation and object in human knowledge but it radically reverses the overall relation of knowledge and reality -- not a Skeptical denial of knowledge as in Hume, but a kind of restructuring of reality itself.

The simplest form of this is familiar enough. Kant believes that our knowledge is of phenomena, the objects of appearance, while reality ultimately is with the things-in-themselves. If we ask what is the most knowable thing for us, the answer in Kant would be mathematics. There are a couple of things about mathematics that put it in this position. (1) Its abstraction. It is easier to know something of abstract rather than concrete content, though if mathematics cannot be completed (according to Gödel), we are limited by the finitude of our knowledge. (2) Kant believes that mathematics is based on the "pure intuition" of space and time, something that underlies phenomenal objects in space and time but does not extend to things-in-themselves. Thus, although Kant sees mathematics as describing the foundations of the phenomenal world, he does not have a Platonic view of mathematics as taking us to the highest levels of reality. Kant might outdo Plato in one respect, saying that mathematics is the "purest" kind of positive human knowledge, owing nothing at all to experience, despite its application being limited to phenomenal objects. For Plato, the purest and highest kind of knowledge would be of the Form of the Good. After mathematics, positive, theoretical knowledge for Kant would mean science. This opens vast expanses, as we have certainly seen since Kant's day.

When it comes to things-in-themselves, Kant believes that the only kind of positive knowledge we can have is by way of morality. Thus, like Plato, priority is given to the good. Kant, however, does not have the kind of concrete and aesthetic view of the good that Plato has. We only know the good by way of the Moral Law, the Categorical Imperative. This is itself a very severe abstraction, based on Kant's view of reason as expressed in the forms of logic, whose application is supposed to generate the imperatives of morality. This is all very dubious, though Kant's good sense overlays it with formulations with more substantive content. Kant then believes that morality provides clues to the Ideas of Reason -- God, freedom, and immorality -- which then give us some notion about realities among thing-in-themselves. Aesthetic value itself is reduced to a subjective sense of the "harmony between the faculties," reconciling theoretical knowledge (science) and practical (morality).

In matters of value, Kant's Copernican reversal does not go as far and is not as consistent as with theoretical knowledge. Aesthetic value, which is resistant to analysis, is presumably less knowable than the abstract content of morality, yet Kant removes it from any connection to external reality at all. Kant's Copernican Revolution in this respect is thus not completed until Jakob Fries. In Fries, we have the distinction between Wissen, Glaude, and Ahndung, where Wissen ("knowledge") is the positive knowledge of mathematics and science, Glaube ("belief") consists of the abstract clues to things-in-themselves that Kant sees in morality, and then Ahndung ("intimation") consists of the positive aesthetic feelings that relate us directly to things-in-themselves. Where Kant only saw religion, "within the limits of reason alone," as consisting of morality, Fries allowed for religion a content of feeling and aesthetic value in addition to that. Needless to say, these aesthetic feelings represent no clear or demonstrable kinds of knowledge.

Although on the right track, the shortcoming of Fries's treatment is that, like Kant's, it is still reductionistic. In the Qur'ân, the Prophet Muhammad denies that he is a poet. Poetry is not prophecy, and religion is not merely art plus morality. Within the framework of Friesian philosophy, this is finally understood by Rudolf Otto. What is characteristic of religion is the sacred or the holy, and the characteristics and feelings associated with this are rather different than the merely aesthetic, or even the aesthetic sense of the sublime. To Otto, one basic feature that will always distinguish the numinous from the merely beautiful or sublime is the uncanny, an eerie sense that seems to accompany something supernatural. The power and splendor of a thunderstorm will seem beautiful, sublime, and terrifying, but it does not convey quite the same kind of fear as a quiet cemetery at night.

Otto thus completes Kant's Copernican Revolution and the reversal of the knowable and the real. Morality now stands in a kind of complete equality with mathematics, yet it does not give rise to the endlessly growing system that mathematics does. Morality has a kind of incompleteness that can only be remedied with a different kind of positive content. Fries returns us to the kind of aesthetic realism found in Plato, while holding that the merely aesthetic is closer to reality than Plato would have allowed (beauty is a clue to the Forms). Finally, Otto identifies something, common to all religion, that is nevertheless difficult to characterize without invoking something contrary to the customary course of nature -- something which thus bespeaks an order beyond the world of experience and science, that which, in the words of the Mandukya Upanishad, is "without an element, what cannot be dealt with or spoken of, the cessation of the phenomenal world, auspicious, nondual."

Here is a graphic I produced for "A New Kant-Friesian System of Metaphysics." This matches up a Friesian metaphysic with the theory of "magnetic substates" in quantum mechanics. It presents a model for how the more knowable varies inversely with the more real. Thus, the long arrow, representing the angular momentum vector in quantum mechanics, might here be called the "moment of necessity." In an absolute sense it is equal for all modes of necessity. However, its component in the z axis varies from the full value (positive or negative) to zero. In atoms, the z axis is identifiable in the presence of a magnetic field (hence "magnetic substates"). Here, the z axis represents the phenomenal world in consciousness, which is a fragment of the reality of things-in-themselves. Thus, the full value of the moment of necessity is apparent to us only where it falls entirely in the phenomenal world, which is the case with logic (analytic necessity) and morality. Otherwise, the vector falls outside the phenomenal world, with a larger or smaller component in it. To the extent that the moment of necessity is not reflected in the z axis, it contains content that is concrete and resistant to abstract analysis. On the side of value, the most familiar case is with beauty, where "there is no disputing taste" (de gustibus non disputandum), but where there nevertheless is at least a hierarchy of taste (since "pushpin" is not as good as poetry, paceJeremy Bentham), and there are regularities of beauty that can identified in a formal and experimental way. On the theoretical side, "conditioned" necessity is the nomological necessity of natural law. If it is possible for the laws of nature to be different in different universes, which is a popular idea these days, then there is an arbitrary element in the natural laws of our universe. Physicists and mathematicians find this offensive, but we are probably stuck with it. The arbitrary element is what cannot be reduced to an abstract formalism. It is less intelligible. For the numinous, the vector's magnitude is only apparent in the transcendent, which leaves its phenomenal content, at zero, entirely irrational and unintelligible. Its presence, of course, is felt in the phenomenal world, which is the difference between a Kantian theory, where phenomena are simply the appearance (in consciousness) of things-in-themselves, and a Platonic theory, where the transcendent is in another world.